cs.ROApr 15, 2026

Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel

Authors: Fumihiko Asano

Organizations: School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

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Abstract

Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.

Figures & tables

Fig. 1: Passive rimless wheel model
Fig. 2: Trajectories of center of mass positions of nonlinear and linearized models
Fig. 3: Trajectories of steady gaits of nonlinear and linearized models in phase space
Fig. 6: 3D plot of T∗(α,ϕ)T^{*}(\alpha,\phi)
Fig. 7: 2D plot of T∗(α,ϕ)T^{*}(\alpha,\phi)
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